As a technique to acquire biological information (e.g., a tomographic image or a three-dimensional image) in a specimen by receiving an ultrasonic wave from the interior of the specimen, there has been an ultrasonic echo, photoacoustic tomography (PAT), and so on. The ultrasonic echo is a method of transmitting an ultrasonic wave to a specimen and receiving its reflected wave. The photoacoustic tomography is a method of transmitting optical energy to the interior of a specimen and receiving an elastic wave (ultrasonic wave) produced as a result of the adiabatic expansion of the specimen due to absorption of the optical energy.
On the other hand, there is also adaptive signal processing which has been developed in the field of radar, etc. A directionally constrained minimization of power (DCMP), being one of adaptive signal processing schemes, is a technique in which when signals are received by a plurality of elements, the plurality of signals thus received are operation processed so as to minimize signal power with the sensitivity in a certain direction (e.g., a direction in which one wants to obtain a signal) being fixed. In adaptive signal processing, a processing parameter for each received signal is adaptively changed (Non Patent Literature (NPL) 1). Such adaptive signal processing is effective in improving spatial resolution, in particular the resolution in the azimuth direction. NPL 2 describes the result of improved resolution obtained by combining such adaptive signal processing with an ultrasonic wave, and NPL 3 describes the result of imaging obtained by combining adaptive signal processing with photoacoustics. As described in NPL 2 and NPL 3, a correlation matrix is first calculated from received signals, and sub-matrices are then extracted therefrom, so that adaptive processing is carried out by the use of a sub-correlation matrix obtained by averaging them. This is a technique shown as spatial smoothing in NPL 4.
In the following, the processing of the DCMP will be described, and then the necessity of using spatial smoothing will be described.
It is assumed that signals have been received by an array having K receiving elements. A signal received by the k-th element is set as xk(t). In this case, a signal group received by the K elements can be denoted by X(t). Here, note that signals are all analytical expressions.X(t)=[x1(t),x2(t), . . . ,xK(t)]T Here, note that a superscript “T” means a transposition. In order to synthesize these signals to generate an output, received signals are multiplied by a complex weight vector W.W=[w1,w2, . . . ,wK]T By this, an output y(t) is obtained.y(t)=WHX(t)=XT(t)W* Here, note that a superscript “H” means a complex conjugate transposition, and a superscript “*” means a complex conjugate.
By changing this complex weight vector to an optimal one according to input signals, an output y is obtained which has been subjected to signal processing in an adaptive manner.
In order to calculate an optimal complex weight vector, a correlation matrix is first calculated based on input signals as follows.Rxx=E[X(t)XH(t)]Here, E[·] means calculating a time average.
In such a state, W under the following conditions is calculated.
            min      W        ⁢          (                        W          H                ⁢                                  ⁢                  R          xx                ⁢        W            )                  subject      ⁢                          ⁢      to      ⁢                          ⁢              W        H            ⁢                          ⁢      a        =    1  These conditions mean minimizing output power with a sensitivity in a desired direction (a direction in which one wants to obtain a signal) being fixed. Here, note that “a” is a steering vector and specifies the desired direction.
When an optimum weight Wopt is calculated under such conditions, the following result is obtained.
  Wopt  =                    R        xx                  -          1                    ⁢      a                      a        H            ⁢                          ⁢              R        xx                  -          1                    ⁢      a      By using this optimum weight, the output power can be minimized with the sensitivity in the desired direction being set to 1. That is, a receiving array using this optimum weight forms a receiving pattern having such a directivity that the sensitivity in the desired direction is set to 1 and the sensitivity in the directions of arrival of noise components is low. In addition, electric power Pout from the desired direction can be expressed as follows.
  Pout  =      1          2      ⁢              a        H            ⁢                          ⁢              R        xx                  -          1                    ⁢      a      The above description until this point states the basic principle of the DCMP.
However, the above-mentioned principle is materialized in cases where a noise component and a desired wave do not have correlativity, but not in cases where a noise component and a desired wave have correlativity. Specifically, in cases where a noise component having correlativity with a desired wave is received, a directive receiving pattern is formed which has a sensitivity of 1 in the direction of the desired wave but a sensitivity in the direction of the noise component at an opposite phase, too. This is because a signal to be output is made near zero so as to minimize the output signal by adding the noise component to the desired wave at the opposite phase.
Incidentally, in cases where imaging is carried out by making use of the transmission and reception of an ultrasonic wave or a photoacoustic effect, a noise component coming in (arriving at) from other than a desired direction has high correlativity with a desired component. This is because in imaging by an ultrasonic wave, the imaging is carried out by the use of reflected waves of an ultrasonic wave that has been transmitted from the element array in order to obtain image information, so a reflected wave from a desired direction and reflected waves reflected from directions other than the desired direction have high correlation. In addition, in imaging by making use of a photoacoustic effect, too, incident light spreads to a wide area due to a scattering effect. Then, in cases where generating causes (absorbers, etc.) for photoacoustic waves of high correlativity (similarity) exist in a specimen, ultrasonic waves generated from such a wide area have a high possibility that they have high correlativity with one another.
A technique that enables the DCMP to operate also on such noise of high correlativity is a spatial smoothing. The spatial smoothing calculates an optimum weight by extracting a plurality of sub-matrices from a correlative matrix as referred to above, and using a sub-correlation matrix which is calculated from an average of the sub-matrices.
A sub-correlation matrix Rpxx can be calculated by the following formulae.
                    X        n            ⁡              (        t        )              =                            [                                                    x                n                            ⁡                              (                t                )                                      ,                                          x                                  n                  +                  1                                            ⁡                              (                t                )                                      ,            …            ⁢                                                  ,                                          x                                  n                  +                  M                  -                  1                                            ⁡                              (                t                )                                              ]                T            ⁢                          ⁢              (                              n            =            1                    ,          2          ,          …          ⁢                                          ,          N                )                        R      pxx        =                  ∑                  n          =          1                N            ⁢                          ⁢                        z          n                ⁢                  E          ⁡                      [                                                            X                  n                                ⁡                                  (                  t                  )                                            ⁢                                                          ⁢                                                X                  n                  H                                ⁡                                  (                  t                  )                                                      ]                              Here, note that N is the number of sub-matrices to be extracted, and M is the size of a sub-matrix obtained at K−N+1. In addition, Zn is a weighting coefficient at the time of averaging the sub-matrices, and the averaging becomes a simple mean at the time of Zn=1/N, but it is also possible to use, as a weighting function, a Hamming window, a Hanning window, a Dolph-Chebycheff window, etc.
By calculating the optimum weight with the use of the sub-correlation matrices Rpxx as mentioned above, it is possible to avoid having sensitivity in the direction of a noise component even if the noise component having high correlativity with a desired wave is received. Therefore, even in cases where an ultrasonic wave is used for transmission and reception, or in the case of imaging by making use of a photoacoustic effect, it becomes possible to obtain the effect due to the DCMP, i.e., the effect of an improvement in the spatial resolution in azimuth direction.
Here, note that Patent Literature (PTL) 1 discloses an apparatus that divides a receiving aperture into sub-apertures, and selects a datum of the smallest output from among those data which have been received at the sub-apertures, respectively, and subjected to similar signal processing.    (PTL 1) Japanese patent application laid-open No. H02-209135    (NPL 1) IEEE Trans. Antennas & Propag. Vol. AP-24, No. 5, pp. 662-669 (September 1976)    (NPL 2) Proc. Acoustics, Speech Signal Process, pp. 489-492 (March 2005)    (NPL 3) OPTICS LETTERS, Vol. 33, No. 12, pp 1291-1293 (Jun. 15, 2008)    (NPL 4) IEEE Trans. Acoust, Speech, Signal Process, Vol. ASSP-33, No. 3, pp. 527-536 (June 1985)